59049 in 10 man and 847288609443 in 25 man
or 3 to the power of the difficulty.
Rolls are not important as each person does not affect the others chances.(there is a calculable odd that everyone rolls and gets loot witch is 0.000017)
It is a system of 10 elements each with 3 different states(not roll,roll and lose,roll and win).The solution to this is in a mathematical formula.

"Never argue with an idiot, they drag you down to their level and then beat you with experience."
-Life

59049 in 10 man and 847288609443 in 25 man
or 3 to the power of the difficulty.
Rolls are not important as each person does not affect the others chances.(there is a calculable odd that everyone rolls and gets loot witch is 0.000017)
It is a system of 10 elements each with 3 different states(not roll,roll and lose,roll and win).The solution to this is in a mathematical formula.

It's unclear exactly what the OP is after, but it seems like we're looking at those that actually used their bonus roll. That means #1 & #2 are out. Then, depending on whether we're looking at everything that's left or just at the scenarios with a win, we have either four possibilities left or we exclude #6. Then we consider there's 10 raiders, and since we're talking about bonus rolls, we can assume independence.

More formally, we can construct a bijection from the set of all distributions of (not roll = A, roll and lose = B, roll and win = C) over a 3 letter alphabet {A,B,C}. Forming 10 letter words for every possible state (the ith letter in the string would correspond to the ith raider's state). Since we can easily enumerate the later, the former holds the same count by the definition bijection.

I think Stede is trying to say that without using a bonus roll, you can win or lose? I don't really understand this, as you can't win or lose a roll that never happened.

I guess I didn't follow that we're only considering the bonus roll and we're not considering the the intial roll at all. That's a pretty straightforward question - straightforward enough that I didn't think anyone would really ask it.

It's unclear exactly what the OP is after, but it seems like we're looking at those that actually used their bonus roll. That means #1 & #2 are out. Then, depending on whether we're looking at everything that's left or just at the scenarios with a win, we have either four possibilities left or we exclude #6. Then we consider there's 10 raiders, and since we're talking about bonus rolls, we can assume independence.

Stede, I thought the question was pretty clear. I did not include the normal rolls, only bonus in the question.

---------- Post added 2013-02-13 at 11:15 AM ----------

OK, anyways this experiment worked out. Look for other Combinatorics Questions in the future.

Looking back on it, it was clear. I just didn't think you'd start a thread about something so rudimentary and slap a label on it that has more syllables than the question has calculation steps.

Well it was just meant to be an elementary counting problem from the Combinatorics branch of Math (Probability & Statistics may also cover this area). Though, you'd be surprised how even something so basic can puzzle very smart people.

59049 in 10 man and 847288609443 in 25 man
or 3 to the power of the difficulty.
Rolls are not important as each person does not affect the others chances.(there is a calculable odd that everyone rolls and gets loot witch is 0.000017)
It is a system of 10 elements each with 3 different states(not roll,roll and lose,roll and win).The solution to this is in a mathematical formula.

This was my thought initially with one difference - we assume *some* of the raiders will use the coin. Doesn't that translate into "not the entire group"?

Well it was just meant to be an elementary counting problem from the Combinatorics branch of Math (Probability & Statistics may also cover this area). Though, you'd be surprised how even something so basic can puzzle very smart people.

Generally, my rule is that, after I spend 5-10 minutes working through something, I go back and make sure I'm reading the question right. Generally. Look forward to more of these.